Question

this figure shows $\triangle xyz$. $\overline{mz}$ is the angle bisector of $\angle yzx$. what is $xm$? enter your answer, as a decimal, in the box. \boxed{} units

Explanation:

Step1: Apply Angle Bisector Theorem

$\frac{XM}{MY} = \frac{XZ}{YZ}$

Step2: Define variable for $XM$

Let $XM = x$, so $MY = 3.5$. Substitute known values:
$\frac{x}{3.5} = \frac{11}{7}$

Step3: Solve for $x$

Multiply both sides by 3.5:
$x = \frac{11}{7} \times 3.5$
Simplify $\frac{3.5}{7} = 0.5$, so $x = 11 \times 0.5$

Answer:

5.5 units